improvement(integrations): tighten sixtyfour, agentmail, agentphone outputs #4765

Bugbot Review

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Final Result: Bugbot completed review - no issues found! ✅

Request ID: serverGenReqId_0b13c780-6e14-4a11-8edd-f7df795f0a91

✅ Bugbot reviewed your changes and found no new issues!

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^{Reviewed by Cursor Bugbot for commit fce28d3. Configure here.}